Twisting Twistor space

TL;DR

This paper develops twisted noncommutative gauge theories on twistor space, establishing their equivalence to four-dimensional noncommutative gauge theories, and constructs noncommutative versions of BF and Chern-Simons theories.

Contribution

It introduces a method to twist twistor space and constructs noncommutative gauge theories, linking them to known four-dimensional theories and extending noncommutative geometry applications.

Findings

Twisted noncommutative gauge theories are equivalent to 4D noncommutative gauge theories.

Constructed noncommutative BF and holomorphic Chern-Simons theories.

Established the role of Poincaré algebra twists in noncommutative twistor space.

Abstract

We construct twisted noncommutative gauge theories on twistor space and show that they are equivalent to four-dimensional twist-noncommutative gauge theories. In particular, we study twists of the Poincar\'e algebra. We explain how such a twist leads to twisted noncommutative twistor space and how to construct noncommutative versions of BF theory and holomorphic Chern-Simons theory on noncommutative supertwistor space. We show how those theories are equivalent to noncommutative versions of Yang-Mills theory and supersymmetric Yang-Mills theory, respectively.